Chapter 5, Problem 111A

To determine

Average velocity of bike.

Answer to Problem 111A

Average velocity of bike is 11.25 km/hr.

Explanation of Solution

Given:

Average velocity of bike is 10 km/hr for 1.5 hour then 15 km/hr for 30 minutes.

Formula used:

Average velocity is given by,

  $v=\frac{d}{t}$

Where,

d is total distance covered.

t is total time taken.

Calculation:

Distance covered by bike in 1.5 hour with a speed of 10 km/hr is,

  $\begin{array}{c}{d}_1=v\times t\\ =10\times 1.5\\ =15\text{ km}\end{array}$

Distance covered by bike in 30 minutes with a speed of 15 km/hr is,

  $\begin{array}{c}{d}_2=v\times t\\ =15\times \frac{30}{60}\\ =15\times 0.5\\ =7.5\text{ km}\end{array}$

Total distance travelled is,

  $\begin{array}{c}d=d_1+d_2\\ =15+7.5\\ =22.5\text{ km}\end{array}$

Total time taken to cover distance d is,

  $\begin{array}{c}t=1.5+0.5\\ =2\text{ hour}\end{array}$

Average velocity is given by,

  $v=\frac{d}{t}$

Now, putting the value of d and t.

  $\begin{array}{c}v=\frac{22.5}{2}\\ =11.25\text{ km/hr}\end{array}$

Conclusion:

Therefore, average velocity of bike is 11.25 km/hr.